Weah, on his first international appearance in 16 years, led the attack and showed glimpses of the class that made him a household name around the world.
He received a standing ovation when he was substituted on 79 minutes.
Goals from Henry Onyekuru and Simeon Nwankwo helped Nigeria to a 2-0 lead before the hosts pulled one back through a Kpah Sherman penalty late in the game.
Weah enjoyed a trophy-laden career in Europe spanning nearly a decade that saw him play for AC Milan in Italy, Monaco, Paris Saint-Germain and Marseille in France, and English sides Manchester City and Chelsea.
As well as being named the 1995 World Footballer of the Year, he also won the Ballon d'Or in the same year and remains the only African to win either award.
Weah's popularity from his playing career saw him secure a landslide win last December in Liberia's presidential elections.
